# .99999999 equal to 1 ??? **URL:** \ **Category:** Factual Questions\ **Created:** [August 15, 2001, 11:42pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468 "2001-08-15T23:42:36Z")\ **Posts on this page:** 7\ **Page:** 11
**Author:** ![DaveW](https://avatars.discourse-cdn.com/v4/letter/d/9d8465/32.png) [@DaveW](https://boards.straightdope.com/u/DaveW)\ **Post date:** [August 21, 2001, 2:29pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/201 "2001-08-21T14:29:05Z")
I was thinking the same thing, Kabbes, except I was working in base 3 (0.1+0.1+0.1=1.0) instead of base 12. Kinda points out the fact that the “difference” between .9rep and 1 is simply how it’s represented on paper (or on a Web site). You just can’t precisely represent certain fractions in base 10. Can’t represent other fractions in base 3. 1/2=0.111rep, for example. Add that result to itself, get 0.222rep, which is, indeed, 1. ---
**Author:** ![kabbes](https://avatars.discourse-cdn.com/v4/letter/k/e99b99/32.png) [@kabbes](https://boards.straightdope.com/u/kabbes)\ **Post date:** [August 21, 2001, 4:36pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/202 "2001-08-21T16:36:08Z")
Alright, I’ll give you that **Dave**. But goddammit - you didn’t spell it out and some people really need it spelled out 🙂 pan ---
**Author:** ![DaveW](https://avatars.discourse-cdn.com/v4/letter/d/9d8465/32.png) [@DaveW](https://boards.straightdope.com/u/DaveW)\ **Post date:** [August 21, 2001, 5:11pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/203 "2001-08-21T17:11:37Z")
Spell which out, **kabbes**? You’re gonna have to spell out what you meant by ‘it’. [cartoon voice]_Oh, pronoun trouble!_[/cartoon voice] 😛 ---
**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\ **Post date:** [August 21, 2001, 5:49pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/204 "2001-08-21T17:49:57Z")
> [@](#): > > \*Originally posted by \*\*\*DaveW \*\* > I was thinking the same thing, Kabbes, except I was working in base 3 (0.1+0.1+0.1=1.0) instead of base 12. Kinda points out the fact that the “difference” between .9rep and 1 is simply how it’s represented on paper (or on a Web site). You just can’t precisely represent certain fractions in base 10. Yes, you can precisely represent 1/3 in base ten. The decimal representation 0.333… specifies that every decimal position is a three. What is imprecise about that? ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [August 21, 2001, 5:55pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/205 "2001-08-21T17:55:44Z")
> [@](#): > > \*Originally posted by DrMatrix \* > \*\* > > > [@](#): > > > > \*Originally posted by \*\*\*DaveW \*\* > > I was thinking the same thing, Kabbes, except I was working in base 3 (0.1+0.1+0.1=1.0) instead of base 12. Kinda points out the fact that the “difference” between .9rep and 1 is simply how it’s represented on paper (or on a Web site). You just can’t precisely represent certain fractions in base 10. > > Yes, you can precisely represent 1/3 in base ten. The decimal representation 0.333… specifies that every decimal position is a three. What is imprecise about that? \*\* I think they don’t really mean “precise”; they mean “without an ellipsis”. ---
**Author:** ![Tretiak](https://avatars.discourse-cdn.com/v4/letter/t/a88e57/32.png) [@Tretiak](https://boards.straightdope.com/u/Tretiak)\ **Post date:** [August 21, 2001, 6:19pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/206 "2001-08-21T18:19:30Z")
You could go about “proving” this another way, although I am not sure how. Assume 0.9999… \< 1 implies 0.9999… + e = 1 for some e \> 0 (a) (b) 1 - .9999… = e 9/10 + 9/100 + 9/1000 + … + e = 1 9/10 + 9/100 + 9/1000 + … + e = 10/10 9/100 + 9/1000 + … + e = 1/10 .0999…+ e = .10000 .999…+ 10e = 1 **10e = 1 - .9999… (from (b)) 10e = e which contradicts (a)** Ok, I know this is really just the same proof offered up differently. But it highlights the infinity part, because without it, the bold section would not be correct. (I realize it is a bit sloppy). ---
**Author:** ![DaveW](https://avatars.discourse-cdn.com/v4/letter/d/9d8465/32.png) [@DaveW](https://boards.straightdope.com/u/DaveW)\ **Post date:** [August 21, 2001, 6:59pm UTC](https://boards.straightdope.com/t/99999999-equal-to-1/76468/207 "2001-08-21T18:59:07Z")
**DrMatrix** wrote: > [@](#): > > Yes, you can precisely represent 1/3 in base ten. The decimal representation 0.333… specifies that every decimal position is a three. What is imprecise about that? Um, what **ultrafilter** said. Sorry about my own lack of precision. [Previous page](https://boards.straightdope.com/t/99999999-equal-to-1/76468.md?page=10)